Final answer:
To find the equation of a parabola passing through three points, set up a system of equations using the coordinates of the points and solve for the variables. Substituting the x and y values of each point into the equation will give you a system of equations to solve.
Step-by-step explanation:
The equation of a parabola passing through three points can be determined by setting up a system of equations using the coordinates of the points. Let's consider the equation of the form y = ax + bx². We can substitute the x and y values of each point into this equation to get three equations. From there, we can solve for a and b.
Using the point (3, 12), we have 12 = 3a + 9b. Using the point (30, -6), we have -6 = 30a + 900b. And using the point (0, 4), we have 4 = 0a + 0b. Solving these equations simultaneously will give us the values of a and b, which we can use to find the equation of the parabola.